THE SOUTHWORTH PLANETARIUM
207-780-4249 www.usm.maine.edu/planet
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70 Falmouth Street Portland, Maine 04103
43.6667° N 70.2667° W
Altitude: 10 feet below sea level
Founded January 1970
Julian Date: 245890.16
"It's a fixer upper of a planet, but we could make it
work."
-Elon Musk
the most hated person in the
astronomical world.
THE DAILY ASTRONOMER
Monday, February 10, 2020
Uranian Gravity
Yes, it's Monday, the weather is dismal, the winter interminable, the
outlook for the week dire, and the cool rains are at this very moment
wicking the crystalline ice away from the trees. One finds that one has
to shovel heaps of coal into the furnace to sustain the cheerful soul
fires. Welcome to the shadowy hollows of mid February. On the other
hand, the Sun is now setting after 5 p.m and even before 6 a.m. the eastern
sky is aglow with pre-dawn twilight. Even now we're seeing the first
signs of the imminent vernal rejuvenation. The awakening world will be
fragrant sooner than we think.
In the meantime, there is always the DA to keep us bucked up and impervious
to the dread.
Today we return to Pandora's Jar for a brilliant question about surface
gravity.
*"I read a list of planet surface gravities. It said that
Uranus's gravity is weaker than Earth. It's a gas giant, so how is that
possible?"*
-Someone who would look a lot like Enya, except for being male, short,
chubby and blond.
Greetings, Someone,
Surface gravity is a tricky matter. We are accustomed to relating gravity
with matter. The more matter an object contains, the more gravitationally
powerful it tends to be. However, with surface gravity, size matters.
With apologies, let me insert a little mathematical formula:
[image: images.png]
g = the surface gravity, G = the Gravitational constant; M is the object's
mass and R is the object's radius. In this equation, the radius is
multiplied by itself.
We can see that the surface gravity is inversely proportional to the size.
As the size increases, the surface gravity decreases. To understand this
inverse proportion, let's pretend you're sitting down, lying down or
standing up. Well, all right, you are probably are sitting, standing or
lying down. Every particle on Earth is pulling on you at the moment.
The rocks beneath your feet, the mountains in New Zealand and even the
ultra hot iron-nickel core. The pull they exert on you depends on their
mass and their distance from you. The farther away they are from you, the
weaker their pull becomes. Or, as Isaac Newton said in his Hillbilly
vernacular:
[image: 71BZz2jEtbL._SX466_.jpg]
*"The magnitude of the gravitational force exerted between two objects is
proportional to the masses of both and inversely proportional to the square
of their separation distance."*
If the planet becomes larger, the distance separating you from the planet's
constituent particles increases and the gravitational force weakens.
The planet Uranus 14.5 times more massive than Earth. However, its radius
is 4 times greater than that of our home planet. Four squared equals
16. Now, if we perform some back of the envelope mathematics. we can
divide 14.5 by 16 and get....well, hold on a moment....just about 0.9.
Uranus' surface gravity is about 0.88 that of Earth as we have to take
oblateness (the way it bulges in the center), its rotational speed and
other complicating factors into account.
A more massive planet doesn't necessarily have a higher surface gravity.
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